MAT 4340/5340 — §101, Spring '14 (141)

Let us reflect that, having banished from our land that religious intolerance under which mankind so long bled and suffered, we have yet gained little if we countenance a political intolerance as despotic, as wicked, and capable of as bitter and bloody persecutions.

— Thomas Jefferson (1743-1826) in his First Inaugural Address.

Homework List

✈ Jump down to '♞ This Week.'

Week 1

Monday, Jan 13 — First day of class
◊ Read Chapter 1.
Wednesday, Jan 15
¤ Group Project: (Due Wednesday, Jan, 22)
Choose one the Edelman Award winners. Find the article describing the winner in the appropriate Jan-Feb issue of Interfaces (Click "Interfaces", then click the "Online Access" link near the bottom of the new page), and write a paragraph or two summarizing the project.
[Some of the articles are in the EdelmanAwards directory.]
Friday, Jan 17
¤ Finish your report on your Group Project.

Week 2

Monday, Jan 20
◊ No class today — Martin Luther King, Jr, Day
Wednesday, Jan 22
◊ Read Chapter 2.
Friday, Jan 24

§3.1, pg. 91. No. 3.1-1, 3.1-4, 3.1-9, 3.1-13. (8th ed)

No. 3.1-2, 3.1-5, 3.1-10, 3.1-14. (9th ed)

Week 3

Monday, Jan 27

§3.2, pg. 91. No. 3.2-1, 3.2-2, 3.2-5, 3.2-6. (8th ed)

No. 3.2-1, 3.2-2, 3.2-5, 3.2-6. (9th ed)

(Hm. Remarkably similar...)
◊ Make sure you know LP terminology.
Wednesday, Jan 29
◊ Set up the Linear Program for the TriCity PowerCo problem in the class slides.
§3.4. No. 3.4-5 (mixed constraint "\(\ge\!/\!\le\)" problem), 3.4-10a (Set up the "Web Mercantile" problem).
Friday, Jan 31
Linear Programming with Excel's Solver:

(8th ed) §3.6, pg. 91. No. 3.6-1acde, 3.6-4abce.

(9th ed) §3.5, pg. 84. No. 3.5-2acde, 3.5-5abce.

Week 4

Monday, Feb 3

(8th ed) §4.1, pg. 162. No. 4.1-1, 4.1-3, 4.1-6.

(9th ed) §4.1, pg. 150. No. 4.1-1, 4.1-3, 4.1-6.
Wednesday, Feb 5

(8th ed) §4.2, pg. 162. No. 4.2-1.

(9th ed) §4.2, pg. 150. No. 4.2-1.
Friday, Feb 7

(8th ed) §4.4, pg. 162. No. 4.4-4, 4.4-6.

(9th ed) §4.4, pg. 150. No. 4.4-4, 4.4-6.
◊ Use the Simplex algorithm to:
\(\begin{align*} \text{Maximize } & Z = 3x_1 + 2x_2 & \\[-3ex] \text{subject to:} \\ &\left\{ \begin{array}{r} 2x_1+\phantom{3}x_2 \le 18 \\ 2x_1+3x_2 \le 42 \\ 3x_1+\phantom{3}x_2 \le 24 \end{array}\right. \\[1ex] \text{with} & \qquad x_i \ge 0 \end{align*}\)

Answer: \(Z(3,12)=33\)

Week 5

Monday, Feb 10

(8th ed) §4.5, pg. 162. No. 4.5-2, 4.5-6.

(9th ed) §4.5, pg. 150. No. 4.5-2, 4.5-4.
◊ Check out the "Online Simplex Tool" (here are some others: SimplexMe.com, EasyCalculation.com)
¤ A "pivot" command for Maple:
- pivot := (M,r,c) -> LinearAlgebra:-RowOperation(LinearAlgebra:-Pivot(M,r,c),r,1/LinearAlgebra:-Pivot(M,r,c)[r,c]^(-1));
Wednesday, Feb 12

(8th ed) §4.6, pg. 162. No. 4.6-1, 4.6-3, 4.6-7ab.

(9th ed) §4.6, pg. 150. No. 4.6-1, 4.6-3, 4.6-7ab.
◊ "O-Jay" exercise from the class notes.
Friday, Feb 14

(8th ed) §4.6, pg. 162. No. 4.6-5, 4.6-8.

(9th ed) §4.6, pg. 150. No. 4.6-5, 4.6-8.
¤ The Tri City Power Group Project is due next Friday, Feb 21.

Week 6

Monday, Feb 17

(8th ed) §4.7, pg. 162. No. 4.7-3d, 4.7-5bc.

(9th ed) §4.7, pg. 150. No. 4.6-3d, 4.7-5bc.
Wednesday, Feb 19
¤ Analyze the shadow prices and reduced costs for the Exercise in Shadow Prices and Reduced Costs notes.
¤ Challenge: Use Excel to produce the reports for the solution of the exercise above.
Friday, Feb 21
¤ Finish your report on your Group Project. (It's due by 5 pm today.)

(8th ed) §6.1, pg. 276. No. 6.1-1, 6.1-3, 6.1-5.

(8th ed) §6.1, pg. 276. No. 6.1-1, 6.1-3, 6.1-5.

(The coeffs are diff in 6.1-5, but the problems are equivalent.)

Week 7

Monday, Feb 24

(8th ed) §5.1, pg. 202. No. 5.1-4.

(9th ed) §5.1, pg. 188. No. 5.1-4.
Wednesday, Feb 26

(8th ed) §8.1, pg. 364. No. 8.1-1, 8.1-2; Look at 8.1-8.

(9th ed) §8.1, pg. 348. No. 8.1-2, 8.1-3; Look at 8.1-9.
Friday, Feb 28
◊ Finish deriving the linear program for the Case Study 4.3. The School Bussing Problem.

Week 8

Monday, Mar 3
◊ Compare the two different solutions from Maple and Excel. How will you present your findings to the school board?
Wednesday, Mar 5
◊ Begin planning for your group's Research Project .
1. Title: Establishing Program Priorities in an Organization Using Analytics
  Abstract: We develop a method for prioritizing programs in an organization using Analytic Hierarchy Process (AHP), a mathematical technique initially developed in the '80s that produces a rank-ordered list of a complete set of programs. AHP builds a stratified ordering with relative priority scores from pairwise assessments using common criteria. The system is based on an eigenanalysis of a positive reciprocal priority matrix in an \(n^2\)-dimensional vector space for \(n\) programs. We simulate an example of prioritizing academic programs with our implementation of AHP using the computer algebra system Maple.
2. Title: An Analytics Method for Ranking Candidates in an Academic Search
  Abstract: We present a procedure for ranking candidates in an academic search using Analytic Hierarchy Process (AHP), a mathematical technique initially developed in the '80s that produces a rank-ordered list of the complete set of acceptable candidates. AHP builds a stratified ordering with relative priority scores from pairwise assessments using common criteria. The system is based on an eigenanalysis of a positive reciprocal priority matrix in an \(n^2\)-dimensional vector space for \(n\) candidates. We simulate ranking and rating candidates for a search with our implementation of AHP using the computer algebra system Maple.
Friday, Mar 7
¤ No class today – ASU is closed due to weather. "Let's be careful out there!"
◊ Work day for the take-home midterm! (See the Class Files directory for the \(\mathrm{\LaTeX}\) files.)
— I'll be in my office around 11:30 and available for questions.

Spring Break Week: Mar 10 → 14.

Week 9

Monday, Mar 17
¤ Finish your test solutions. Regular homework resumes Wednesday...
Wednesday, Mar 19
◊ Your take-home test solutions are due today!
¤ Replace the Saturn in the "Canonical First Example" in the Analytic Hierarchy Process notes with your choice of car. Perform an AHP analysis to rank the four cars. Which one should you purchase?
Friday, Mar 21
◊ No homework — Happy Birthday to Ralph!

Week 10

Monday, Mar 24
◊ AHP Homework Problem:

Joan is graduating from Appalachian this spring. She is trying to determine which job to accept, and has chosen four objectives:

High starting salary
Quality of life in the city where the job is located
Interest level in the type of work
Nearness to family

Using the four (partial) assessment matrices shown below, and your own \(4\times4\) priority matrix for her objectives, give Joan a ranking for her three choices, Job 1, Job 2, and Job 3, along with a consistency rating.

Salary Comparisons
	Job 1	Job 2	Job 3
Job 1	1	2	4
Job 2	__	1	2
Job 3	__	__	1

Quality of Life Comparisons
	Job 1	Job 2	Job 3
Job 1	1	1/2	1/3
Job 2	__	1	1/3
Job 3	__	__	1

Interest of Work Comparisons
	Job 1	Job 2	Job 3
Job 1	1	1/7	1/3
Job 2	__	1	3
Job 3	__	__	1

Closeness to Family Comparisons
	Job 1	Job 2	Job 3
Job 1	1	1/4	1/7
Job 2	__	1	1/2
Job 3	__	__	1

Wednesday, Mar 26
◊ Research project workflow
¤ \(\LaTeX\) poster resources

Friday, Mar 28
¤ Research Project day — Get your team together; plan your work flow; get started.

Academic Search

Criteria List
The nine Colleges are: Arts & Sciences, Fine & Applied Arts, Health Sciences, Music, Honors College, Education, University College, Business, and the Graduate School.
- Randomly choose one department in each college to supply a faculty representative
- Randomly choose one College Dean to chair the committee

Your committee has received 15 applications:

1. Dr Sofia Kovalevsky,	2. Dr Jules Poincare,	3. Dr Andrei Markov,	4. Dr Giuseppe Peano,	5. Dr David Hilbert,
6. Dr Henri Lebesgue,	7. Dr Emma Noether,	8. Dr George Birkhoff,	9. Dr George Polya,	10. Dr Emil Artin,
11. Dr Alan Turing,	12. Dr Rosemary Bailey,	13. Dr John Conway,	14. Dr Kurt Godel,	15. Dr Felix Borel

Their credentials are forthcoming.

Academic Program Priorities

The "Big Criteria List" (Choose 2 items from each of the 5 sections. Make sure to choose a few 'objective' criteria.)

Randomly choose a 9 faculty representatives covering the Arts & Sciences areas with the Dean as committee chair.

Humanities

English
Languages, Literatures and Cultures
Philosophy and Religion

Social Sciences

Anthropology
Geography and Planning
Government & Justice Studies
History
Psychology
Sociology

STEM

Biology
Chemistry
Computer Science
Geology
Mathematical Sciences
Physics and Astronomy

Each department is considered a single program for this "prioritization exercise."

Extra resources:
- The Official Guidelines for Undergraduate Program Prioritization
- The Chancellor's Report
- The Insitutional Research website with program data

Maple worksheet to generate random vectors with a specified distribution

The Office of Student Research is pleased to announce that the 17th Annual Celebration of Student Research and Creative Endeavors will take place on

from 9:00 am - 5:00 pm on the fourth floor of the new Plemmons Student Union Addition.

Week 11

Monday, Mar 31
◊ Project work day
Wednesday, Apr 2
◊ Generating random vectors with given distributions in Maple
Friday, Apr 4
◊ The \(\mathrm{\LaTeX}\) templates ("AHP Poster\(\cdots\).zip") are in the AHP directory inside the Class Notes directory.

Week 12

Monday, Apr 7
¤ The posters are excellent! Well done, Teams.
- Establishing Program Priorities in an Organization Using Analytics
- An Analytics Method for Ranking Candidates in an Academic Search
Wednesday, Apr 9

(8th ed) §9.3 & 4, pg. 428. No. 9.3-1ab, 9.3-3, 9.4-1.

(9th ed) §9.3 & 4, pg. 412. No. 9.3-2ab, 9.3-4, 9.4-1.
Thursday, Apr 10 — ¡Poster Day!
¤ 1:00–4:00 pm, PSU, Parkway Ballroom, Room 420
Friday, Apr 11
◊ PERT/CPM exercise from the class notes.

Week 13

Monday, Apr 14
◊ Produce the CPM graph with node values \(ES_i\) and \(LC_j\) for the PERT/CPM problem we considered in class today.

Grad Student Presentation Topics
Data Envelopment Analysis	Decision Trees for Drug Testing (KT)	Financial Models (AM)
Generating Random Numbers for Simulations (MJ)	Genetic Algorithms (TM)	Markov Chains (RC)
Queueing Theory (HT)	Simulated Annealing (KJ)	Stochastic Models
Time Series Analysis	Game Theory (LT)	[UNC's] Ph.D. Program(s) in O.R. (TW)
Sample Presentation Rubric

Wednesday, Apr 16

(8th ed) §18.3 & 4, pg. 891. No. 18.3-1a, 18.3-2a.

(9th ed) §18.3 & 4, pg. 892. No. 18.3-1a, 18.3-2a.
Friday, Apr 18

(8th ed) §18.3 & 4, pg. 891. No. 18.3-9.

(9th ed) §18.3 & 4, pg. 892. No. 18.3-9.
◊ A Math Career note from Analytics magazine for a quick Easter Break read.
◊ There are lots of analytics jobs to apply for...

Week 14

Monday, Apr 21 — Easter Break
¤ No classes.
Wednesday, Apr 23 — Happy 450th Birthday to Shakespeare...
◊ Read the Data Envelopment Analysis Tutorial by Vasilis Vryniotis.
◊ Look at the DEA Bibliography (covering '78 through '01)
Friday, Apr 25
◊ Apportionment slides
¤ Design a measure to indicate the degree of "gerrymandering".

Week 15

Monday, Apr 28
¤ Presentations:
- Game Theory - LK
- Markov Process - RC
Wednesday, Apr 30
¤ Presentations.
- Generating Random Numbers - MJ
- PhD in OR at UNC - TW
◊ The final exam. (The \(\mathrm{\LaTeX}\) source.)
Congressional District Maps (from Maple)
Friday, May 2
¤ Last day of classes.
◊ Work day for your final exam solutions.

Week 16 ♞ (This Week)

Wednesday, May 7
◊ Final Exam from 3:00 – 5:30 PM

“On two occasions I have been asked, ‘Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?’ I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.”

— Charles Babbage in Passages from the Life of a Philosopher

Last modified: Wednesday, 01-Feb-2023 08:32:12 EST

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§3.1, pg. 91.	No. 3.1-1, 3.1-4, 3.1-9, 3.1-13. (8th ed)
	No. 3.1-2, 3.1-5, 3.1-10, 3.1-14. (9th ed)

§3.2, pg. 91.	No. 3.2-1, 3.2-2, 3.2-5, 3.2-6. (8th ed)
	No. 3.2-1, 3.2-2, 3.2-5, 3.2-6. (9th ed)
	(Hm. Remarkably similar...)

(8th ed)	§3.6, pg. 91.	No. 3.6-1acde, 3.6-4abce.
(9th ed)	§3.5, pg. 84.	No. 3.5-2acde, 3.5-5abce.

(8th ed)	§4.1, pg. 162.	No. 4.1-1, 4.1-3, 4.1-6.
(9th ed)	§4.1, pg. 150.	No. 4.1-1, 4.1-3, 4.1-6.

(8th ed)	§4.2, pg. 162.	No. 4.2-1.
(9th ed)	§4.2, pg. 150.	No. 4.2-1.

(8th ed)	§4.4, pg. 162.	No. 4.4-4, 4.4-6.
(9th ed)	§4.4, pg. 150.	No. 4.4-4, 4.4-6.

(8th ed)	§4.5, pg. 162.	No. 4.5-2, 4.5-6.
(9th ed)	§4.5, pg. 150.	No. 4.5-2, 4.5-4.

(8th ed)	§4.6, pg. 162.	No. 4.6-1, 4.6-3, 4.6-7ab.
(9th ed)	§4.6, pg. 150.	No. 4.6-1, 4.6-3, 4.6-7ab.

(8th ed)	§4.6, pg. 162.	No. 4.6-5, 4.6-8.
(9th ed)	§4.6, pg. 150.	No. 4.6-5, 4.6-8.

(8th ed)	§4.7, pg. 162.	No. 4.7-3d, 4.7-5bc.
(9th ed)	§4.7, pg. 150.	No. 4.6-3d, 4.7-5bc.

(8th ed)	§6.1, pg. 276.	No. 6.1-1, 6.1-3, 6.1-5.
(8th ed)	§6.1, pg. 276.	No. 6.1-1, 6.1-3, 6.1-5.
		(The coeffs are diff in 6.1-5, but the problems are equivalent.)

(8th ed)	§8.1, pg. 364.	No. 8.1-1, 8.1-2; Look at 8.1-8.
(9th ed)	§8.1, pg. 348.	No. 8.1-2, 8.1-3; Look at 8.1-9.

(8th ed)	§9.3 & 4, pg. 428.	No. 9.3-1ab, 9.3-3, 9.4-1.
(9th ed)	§9.3 & 4, pg. 412.	No. 9.3-2ab, 9.3-4, 9.4-1.

(8th ed)	§18.3 & 4, pg. 891.	No. 18.3-1a, 18.3-2a.
(9th ed)	§18.3 & 4, pg. 892.	No. 18.3-1a, 18.3-2a.

(8th ed)	§5.1, pg. 202.	No. 5.1-4.
(9th ed)	§5.1, pg. 188.	No. 5.1-4.

(8th ed)	§18.3 & 4, pg. 891.	No. 18.3-9.
(9th ed)	§18.3 & 4, pg. 892.	No. 18.3-9.